When the frictionless system shown below is accelerated by an applied force of magnitude the tension in the string between the blocks is
Correct answer: D. 1/3 F
- A. F
- B. 2/3 F
- C. ½ F
- D. 1/3 F
Explanation
The correct answer is 1/3 F. In a frictionless system, the acceleration of the entire system is given by a = F / mtotal. The tension, FT, is equal to the applied force multiplied by the ratio of the mass behind the rope to the total mass being pulled. This translates to FT = (Mbehind the rope / mtotal) * F. If the mass behind the rope is one-third of the total mass, then the tension in the string is 1/3 F.Option A, F, assumes no internal distribution of force which is incorrect. Option B, 2/3 F, and Option C, ½ F, do not correctly consider the precise distribution of masses in the system.
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